Whakaoti i te (7+z)(9-z)+(7-z)(9+z)=76

$$( 7 + z ) ( 9 - z ) + ( 7 - z ) ( 9 + z ) = 76$$

Whakaoti mō z

$$z=5$$

$$z=-5$$

Ngā Upane mā te Kimi Pūtakerua

Whakamahia te āhuatanga tuaritanga hei whakarea te 7+z ki te 9-z ka whakakotahi i ngā kupu rite.

$$63+2z-z^{2}+\left(7-z\right)\left(9+z\right)=76$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 7-z ki te 9+z ka whakakotahi i ngā kupu rite.

$$63+2z-z^{2}+63-2z-z^{2}=76$$

Tāpirihia te 63 ki te 63, ka 126.

$$126+2z-z^{2}-2z-z^{2}=76$$

Pahekotia te 2z me -2z, ka 0.

$$126-z^{2}-z^{2}=76$$

Pahekotia te -z^{2} me -z^{2}, ka -2z^{2}.

$$126-2z^{2}=76$$

Tangohia te 126 mai i ngā taha e rua.

$$-2z^{2}=76-126$$

Tangohia te 126 i te 76, ka -50.

$$-2z^{2}=-50$$

Whakawehea ngā taha e rua ki te -2.

$$z^{2}=\frac{-50}{-2}$$

Whakawehea te -50 ki te -2, kia riro ko 25.

$$z^{2}=25$$

Tuhia te pūtakerua o ngā taha e rua o te whārite.

$$z=5 z=-5$$

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Whakamahia te āhuatanga tuaritanga hei whakarea te 7+z ki te 9-z ka whakakotahi i ngā kupu rite.

$$63+2z-z^{2}+\left(7-z\right)\left(9+z\right)=76$$

Whakamahia te āhuatanga tuaritanga hei whakarea te 7-z ki te 9+z ka whakakotahi i ngā kupu rite.

$$63+2z-z^{2}+63-2z-z^{2}=76$$

Tāpirihia te 63 ki te 63, ka 126.

$$126+2z-z^{2}-2z-z^{2}=76$$

Pahekotia te 2z me -2z, ka 0.

$$126-z^{2}-z^{2}=76$$

Pahekotia te -z^{2} me -z^{2}, ka -2z^{2}.

$$126-2z^{2}=76$$

Tangohia te 76 mai i ngā taha e rua.

$$126-2z^{2}-76=0$$

Tangohia te 76 i te 126, ka 50.

$$50-2z^{2}=0$$

Ko ngā tikanga tātai pūrua pēnei i tēnei nā, me te kīanga tau x^{2} engari kāore he kīanga tau x, ka taea tonu te whakaoti mā te whakamahi i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, ina tuhia ki te tānga ngahuru: ax^{2}+bx+c=0.

$$-2z^{2}+50=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi -2 mō a, 0 mō b, me 50 mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-2\right)\times 50}}{2\left(-2\right)}$$

Pūrua 0.

$$z=\frac{0±\sqrt{-4\left(-2\right)\times 50}}{2\left(-2\right)}$$

Whakareatia -4 ki te -2.

$$z=\frac{0±\sqrt{8\times 50}}{2\left(-2\right)}$$

Whakareatia 8 ki te 50.

$$z=\frac{0±\sqrt{400}}{2\left(-2\right)}$$

Tuhia te pūtakerua o te 400.

$$z=\frac{0±20}{2\left(-2\right)}$$

Whakareatia 2 ki te -2.

$$z=\frac{0±20}{-4}$$

Nā, me whakaoti te whārite z=\frac{0±20}{-4} ina he tāpiri te ±. Whakawehe 20 ki te -4.

$$z=-5$$

Nā, me whakaoti te whārite z=\frac{0±20}{-4} ina he tango te ±. Whakawehe -20 ki te -4.

$$z=5$$

Kua oti te whārite te whakatau.

$$z=-5 z=5$$